Comparing a British payslip with an American one
British gross pay carries income tax under PAYE, National Insurance contributions, and student loan repayments where a plan applies. The bands differ between Scotland and the rest of the UK, so where you live inside the country changes the answer. An American payslip carries federal withholding, state withholding where the state levies it, and the federal payroll taxes, with health cover normally bought outside the payslip.
As with any transatlantic comparison, the healthcare difference sits underneath the numbers rather than in them. The British deductions include a contribution to a system that provides care; the American net figure has not yet paid for the equivalent. A comparison of take-home pay alone therefore favours the American side by an amount that does not appear anywhere on this page.
Equal purchasing power, not the exchange rate
The second gross salary shown is the one that buys the same basket in the other place, derived from official purchasing power parities rather than from the sterling exchange rate. Both sides then go through their own withholding rules, and the resulting net pay is brought back to a single set of prices in the row labelled real take-home. Because both columns start from the same real income, what separates them at the end is the tax systems and nothing else.
Where one side is a US state, its price level is chained rather than measured: Eurostat publishes a parity for the United States as a whole, the Bureau of Economic Analysis publishes an index placing each state against the American average, and the state figure is the first scaled by the second. The page notes this above the tables. It is the standard construction and it still rests on one assumption more than a country-to-country comparison does.
The exchange rate is shown as a dated contrast line. It answers a different question, namely what a bank would give you for the money, and it is the number that makes cross-border offers look better or worse than they are.